I had a supra-pubic catheter, which comes out just above the penis and below the belt line. Not as bad as a urethral catheter, but they are all a bloody nuisance.
After three or four days you’ll get used to it and all the horrible pipework and literally pissing about. You should then be able to sleep on the side of your choice.
Only a short time to removal, so grin and bear it.
Best of luck.